Prime Distance Labeling of the Non- Commuting Graph of Some Non-Abelian Groups

A graph G(V, E) is said to admit a prime distance labeling if there exists an oneto-one function h ∶ V (G) → Z such that |h(u) − h(v)| is a prime number for every pair of adjacent vertices u and v in G . In this paper, we investigate if the prime distance labeling of the non-commuting graph of non-abelian groups such as symmetric group (Sn, o), dihedral group D2n, n ∈ N exists or not.